Titelaufnahme

Titel
Inverse problems in spaces of measures
Verfasser/ VerfasserinBredies, Kristian ; Pikkarainen, Hanna Katriina
Erschienen in
Erschienenedp sciences
Ausgabe
Preprint
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Inverse problems / vector-valued nite Radon measures / Tikhonov regularization theory / delta-peak solutions / generalized conditional / gradient method / iterative soft-thresholding / sparse deconvolution
ISSN1292-8119
URNurn:nbn:at:at-ubg:3-314 Persistent Identifier (URN)
DOIdoi:10.1051/cocv/2011205 
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Inverse problems in spaces of measures [0.79 mb]
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Zusammenfassung (Englisch)

The ill-posed problem of solving linear equations in the space of vector-valued finite Radon measures with Hilbert space data is considered. Approximate solutions are obtained by minimizing the Tikhonov functional with a total variation penalty. The well-posedness of this regularization method and further regularization properties are mentioned. Furthermore, a flexible numerical minimization algorithm is proposed which converges subsequentially in the weak* sense and with rate (n-1) in terms of the functional values. Finally, numerical results for sparse deconvolution demonstrate the applicability for a finite-dimensional discrete data space and infinite-dimensional solution space.

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